Reduce to lowest terms: $ \dfrac{1}{6} \div - \dfrac{5}{9} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{5}{9}$ is $- \dfrac{9}{5}$ Therefore: $ \dfrac{1}{6} \div - \dfrac{5}{9} = \dfrac{1}{6} \times - \dfrac{9}{5} $ $ \phantom{ \dfrac{1}{6} \times - \dfrac{9}{5}} = \dfrac{1 \times -9}{6 \times 5} $ $ \phantom{ \dfrac{1}{6} \times - \dfrac{9}{5}} = \dfrac{-9}{30} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-9}{30} = \dfrac{-9 \div 3}{30 \div 3} = -\dfrac{3}{10} $